Wine and water:

if we assume there are no volume effects from mixing, then it is obvious that the amount of water in the wine must be exactly the same as the amount of wine in the water.

At the beginning we have two pints (or litres or liters or whatever) of liquid, exactly one half is water, exactly one half is wine.

At the end, we have two pints (or ...) of liquid. Still exactly one half is water and exactly the other half is wine.

As both containers contain exactly half of the liquid (one tablespoon of liquid was moved from A to B, and then one tablespoon was moved from B to A), whatever amount of water is missing from container A is now in container B. And, as we assumed no volume effects from mixing, exactly the same amount of wine is now in container A.

Unless someone has turned water into wine ...